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A Robust Estimation for the Composite Lognormal-Pareto Model
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 Title & Authors
A Robust Estimation for the Composite Lognormal-Pareto Model
Pak, Ro Jin;
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 Abstract
Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.
 Keywords
Lognormal distribution;maximum likelihood estimation;minimum distance estimation;Pareto distribution;
 Language
English
 Cited by
 References
1.
Basu, A., Harris, I. R., Jort, N. L. and Jones, M. C. (1998). Robust and efficient estimation by minimizing a density power divergence, Biometrika, 85, 549-559. crossref(new window)

2.
Cooray, K. and Ananda, M. M. A. (2005). Modeling actuarial data with a composite lognormal-Pareto model, Scandinavian Actuarial Journal, 5, 321-334.

3.
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions, John Wiley and Sons, New York.

4.
Hogg, R. V. and Klugman, S. A. (1984). Loss Distribution, John Wiley and Sons, New York.

5.
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (1998). Loss Models From Data to Decisions, John Wiley and Sons, New York.

6.
McNeil, A. (1997). Estimating the tails of loss severity distributions using extreme value theory, ASTIN Bulletin, 27, 117-137. crossref(new window)

7.
Pigeon, M. and Denuit, M. (2011). Composite Lognormal-Pareto model with random threshold, Scandinavian Actuarial Journal, 3, 177-192.

8.
Resnick, S. I. (1997). Discussion of the Danish data on large fire insurance losses, ASTIN Bulletin, 27, 139-151. crossref(new window)

9.
Ricci, V. (2005). Fitting Distributions with R, http://cran.r-project.org.

10.
Scollnik, D. P. (2007). On composite lognormal-Pareto models, Scandinavian Actuarial Journal, 1, 20-33.